Evaluating performance metrics is a fundamental problem when there are multiple media channels and changes are needed in the use of multiple media channels to maximize one or more performance metric. Many entities use multiple media channels to maximize their performance metrics. Media mix modeling (“MMM”) is an analytical approach (e.g., multivariate regression) using observational data to estimate and forecast the impact of various media mix strategies on performance metrics. One performance metric may be return on ad spend (“ROAS”).